Place one decimal above the other so that they are lined up on the right side.
Draw a line under the bottom number. Temporarily disregard the decimal points and
multiply the numbers like you would multiply a three digit number by a two digit number.

0.529
0.67

Multiply the two numbers on the right side. (9 * 7 = 63). This number is larger
than 9 so place a 6 above the center column and place a 3 below the
line in the right column.

6
0.529 0.673

Multiply the digit in the top center column (2) by the digit in the lower right
column (7). The answer (2*7=14) is added to the 6 above the center
column to give an answer of 20. The 0 of 20 is placed below the line and the 2 of the
20 is placed above the 5.

26
0.529
0.6703

The 5 of the top number is multiplied by the 7 of the lower multiplier
(5*7=35). The two that was previously carried
is added and the 37 is placed below the line.

26
0.529
0.673703

After 529 has been multiplied by 7 as shown above, 529 is multiplied by the 6
of the multiplier. The number is moved one place to the left. The result would be
3174:

15
0.529
0.67
3703
3174

A line is drawn under the lower product (3174) and the products are added
together to get the final answer of 35443. At the start we disregarded the decimal
points. We must now count up the decimal places and move the decimal place to its
proper location. We have three decimal places in 0.529 and two in the decimal 0.67 so
we move the decimal five places to the left to give the final answer of 0.35443.